Differential Flatness of Slider–Pusher Systems for Constrained Time Optimal Collision Free Path Planning

Abstract

In this work, we show that the differential kinematics of slider–pusher systems are differentially flat assuming quasi-static behavior and frictionless contact. Second, we demonstrate that the state trajectories are invariant to time-differential transformations of the path parametrizing coordinate. For one this property allows to impose arbitrary velocity profiles on the slider without impacting the geometry of the state trajectory. This property implies that certain path planning problems may be decomposed approximately into a strictly geometric path planning and an auxiliary throughput speed optimization problem. Building on these insights, we elaborate a numerical approach tailored to constrained time optimal collision free path planning and apply it to the slider–pusher system.